Single DNA conformations and biological function Ralf Metzler∗ NORDITA—Nordic Institute for Theoretical Physics, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark and Department of Physics, University of Ottawa, 150 Louis Pasteur, Ottawa, Ontario, K1N 6N5, Canada (New address) Tobias Ambj¨ornsson NORDITA—Nordic Institute for Theoretical Physics, Blegdamsvej 17, 2100 Copenhagen Ø, Denmark and Department of Chemistry, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139 (New address) Andreas Hanke Department of Physics and Astronomy, University of Texas at Brownsville, 80 Fort Brown, Brownsville, TX 78520 and Institute of Biomedical Sciences and Technology, University of Texas at Dallas, Richardson, TX 75083 Yongli Zhang Department of Physiology and Biophysics, Albert Einstein College of Medicine, Bronx, NY 10461 Stephen Levene Institute of Biomedical Sciences and Technology and Department of Molecular and Cell Biology, University of Texas at Dallas, Richardson, TX 75083 Abstract. From a nanoscience perspective, cellular processes and their reduced in vitro imitations provide extraordinary examples for highly robust few or single molecule reaction pathways. A prime example are biochemical reactions involving DNA molecules, and the coupling of these reactions to the physical conformations of DNA. In this review, we summarise recent results on the following phenomena: We investigate the biophysical properties of DNA-looping and the equilibrium configurations of DNA-knots, whose relevance to biological processes are increasingly appreciated. We discuss how random DNA-looping may be related to the efficiency of the target search process of proteins for their specific binding site on the DNA molecule. And we dwell on the spontaneous formation of intermittent DNA nanobubbles and their importance for biological processes, such as transcription initiation. The physical properties of DNA may indeed turn out to be particularly suitable for the use of DNA in nanosensing applications. Key words: DNA, single molecules, DNA looping, DNA denaturation, knots, gene regulation ∗Electronic address: [email protected] arXiv:physics/0609139v2 [physics.bio-ph] 14 Nov 2006 2 Contents I. Introduction 3 II. Physical properties and biological function of DNA 4 III. DNA-looping 7 A. Biological significance of DNA looping 7 B. DNA loop model 9 C. Simplified protein geometries and flexibility parameters 9 D. DNA loops having zero end-to-end distance and antiparallel helical axes 9 E. DNA looping with finite end-to-end distance, antiparallel helical axes, and in-phase torsional constraint 10 F. DNA looping in synapsis 11 G. Conclusion 13 IV. DNA knots and their consequences: entropy and targeted knot removal 13 A. Physiological background of knots 13 B. Classification of knots 15 C. Long chains are almost always entangled. 16 D. Entropic localisation in the figure-eight slip-link structure. 16 E. Simulations of entropic knots in 2D and 3D. 18 F. Flattened knots in dilute and dense phases. 20 1. Flat knots in dilute phase. 21 2. Flat knots under Θ and dense conditions. 23 G. 3D knots defy complete analytical treatment. 25 V. DNA breathing: local denaturation zones and biological implications 26 A. Physiological background of DNA denaturation 26 B. The Poland-Scheraga model of DNA melting 28 C. Fluctuation dynamics of DNA bubbles: DNA breathing 30 D. Probabilistic modelling—the master equation (ME) 31 E. Stochastic modelling—the Gillespie algorithm 32 F. Bacteriophage T7 promoter sequence analysis. 33 G. Interaction of DNA bubbles with selectively single-strand binding proteins 34 VI. Role of DNA conformations in gene regulation 35 A. Physiological background of gene regulation and expression 35 B. Binding proteins: Specific and nonspecific binding modes 36 C. The search process for the specific target sequence 37 D. A unique situation: Pure one-dimensional search of SSB mutants 38 E. L´evy flights and target search 38 F. Viruses—extreme nanomechanics 40 VII. Functional molecules and nanosensing 40 A. Functional molecules 40 B. Nanosensing 41 VIII. Summary 42 Acknowledgments 42 Biographical notes 43 A polymer primer. 45 Polymer networks. 46 References 48 3 I. INTRODUCTION in the virus capsid and prevent ejection of the DNA into a host, and thereby infection. DNA knots are also be- Deoxyribonucleic acid (DNA) is the molecule of life ing recognised as a potential complication in the use of as we know it.1 It contains all information of an entire nanochannels for DNA separation and sequencing. In organism.2 This information is copied during cell divi- such confined geometries DNA knots are created with sion with an extremely high fidelity by the replication appreciable probability, affecting the reliability of these mechanism. Despite the rather high chemical and phys- techniques. Similarly to DNA knots, DNA looping is ical stability of DNA, due to constant action of enzymes intimately connected to the function of DNA. Current and other binding proteins (mismatches, rupture) as well results on DNA looping and DNA knot behaviour are as potential environmentally induced damage (radiation, summarised in the first parts of this review. chemicals), this low error rate, i.e., the suppression of the The Watson-Crick double-helix represents the thermo- liability to mutations, is only possible with the constant dynamically stable state of DNA at moderate salt con- action of repair mechanisms (1; 2; 3; 4). Although DNA’s centrations and below the melting temperature. This structural and mechanical properties are rather well es- stability is effected by Watson-Crick hydrogen bonding tablished for isolated DNA molecules (starting with Ros- and the stronger base stacking of neighbouring base-pairs alind Franklin’s X-ray diffraction images (5)), the charac- (bps). However, even at room temperature DNA locally terisation of DNA in its cellular environment, and even in opens up intermittent flexible single-stranded domains, vitro during interaction with binding proteins, is subject so-called DNA-bubbles. Their size typically ranges from of ongoing investigations. a few broken bps, increasing to some 200 broken bps Recent advances in experimental techniques such as closer to the melting temperature. The thermal melt- fluorescence methods, atomic force microscopy, or opti- ing of DNA has traditionally been used to obtain the cal tweezers have leveraged the potential to both probe sequence-dependent stability parameters of DNA. More and manipulate the equilibrium and out of equilibrium recently, the role of intermittent bubble domains has behaviour of single DNA molecules, making it possible been investigated with respect to the liability of DNA- to explore DNA’s physical and mechanical properties as denaturation induced by proteins that selectively bind to well as its interaction with other biopolymers, such as the single-stranded DNA. It has been speculated that due to DNA-protein interplay during gene regulation or repair the liability to denaturation of the TATA motif bubble processes. An important ingredient is the coupling to formation may add in transcription initiation. The dy- thermal activation due to the highly Brownian environ- namics of single bubbles can be monitored by fluorescence ment. Although mostly performed in vitro, these exper- methods, opening a window to both study the breathing iments provide access to increasingly refined information of DNA experimentally, but also to obtain high precision on the nature of DNA and its environment-controlled be- DNA stability data. Finally, bubble dynamics has been haviour. suggested as a useful tool in optical nanosensing. DNA In addition to chromosomal packaging inside the nu- breathing is the topic of the second part of this work. cleus of eukaryotic cells and the concentration of DNA Essentially all the biological functions of DNA rely on in the membraneless nucleoid region of prokaryotes, the site-specific DNA-binding proteins locating their targets global structure of the DNA molecule can be affected (cognate sites) on the DNA molecule, and therefore re- by topological entanglements. Thus, by error or design quire searching through megabases of non-target DNA in a DNA molecule can attain a knotted or concatenated a highly efficient manner. For instance, gene regulation state, reducing or inhibiting biologically relevant func- is performed by specific regulatory proteins. On binding tions, for instance, replication or transcription. Such en- to a promoter area on the DNA, they recruit or inhibit tangled states can be actively reduced by enzymes of the binding of RNA polymerase and subsequent transcrip- topoisomerase family. Their precise action, in particular, tion of the associated gene. The search for the cognate how they determine the presence of an entangled state, is site is in fact facilitated by the DNA molecule: in addi- not fully known. Current studies therefore aim at shed- tion to three-dimensional search it enables the proteins ding light on possible mechanisms, in particular, in view to also move one-dimensionally along the DNA while be- of the importance of topoisomerase action (or better, its ing non-specifically bound. Moreover, at points where inhibition) in tumour proliferation. Other applications the DNA loops back on itself, this polymeric conforma- may be directed towards the treatment of viral deceases tion provides shortcuts for the proteins in the chemical by modifying the packaging of viral DNA to create knots coordinate along the DNA, approximately giving rise to search-efficient L´evy